An object 2 cm high is placed at a distance of 64 cm from a white screen. On placing a convex lens at a distance of 32 cm from the object it is found that a distinct image of the object is formed on the screen. What is the size of the image formed on the screen?

To solve this problem, we need to use the lens formula and magnification formula.

The lens formula is 1/f = 1/v - 1/u, where f is the focal length of the lens, v is the image distance, and u is the object distance.

Given that the object is placed 32 cm from the lens (u = -32 cm, the negative sign indicates that the object is on the same side of the lens as the light being used), and the image is formed on the screen which is 64 cm from the object, so the image distance v = 64 - 32 = 32 cm.

Substituting these values into the lens formula, we get:

1/f = 1/32 - 1/(-32) 1/f = 1/32 + 1/32 1/f = 2/32 f = 32/2 = 16 cm

The magnification (m) of the lens is given by the ratio of the height of the image (h') to the height of the object (h), and is also equal to the ratio of the image distance to the object distance (-v/u).

So, m = h'/h = -v/u

We know that h = 2 cm, v = 32 cm, and u = -32 cm. Substituting these values in, we get:

m = h'/2 = -32/-32 h' = 2 * 1 = 2 cm

So, the size of the image formed on the screen is 2 cm.